What levels should I have my Pokemon to beat the gym leaders?

Here some help:

First Gym Leader (Brock) - Level 15
Second Gym Leader (Misty) - Level 22
Third Gym Leader (Surge) - Level 25
Fourth Gym Leader (Erika) - Level 30
Fifth Gym Leader (Koga) - Level 45
Sixth Gym Leader (Sabrina) - Level 45
Seventh Gym Leader (Blaine) - Level 50
Eighth Gym Leader (Giovanni) - Level 55

The Levels that I have listed are what I would recommend you have your Pokemon be when they're facing a certain Gym Leader. These Levels are higher than the Gym Leaders' Pokemon. I recommend this so you don't have too hard of a time when facing them.

Hope this helps!

Felicia

My Pokemon Red journey was a little weird.
I started with six Pokemon byt changed later in the game. My final team was Level 55 Zapdos, level 53 Articuno, level 51 moltres, level 45 charizard, level 50 blastoise, level 41 nidoking. Catch a least one of the legendary birds at least. It helped me a lot.

Rock gym: 16 or 17

Water gym: 23 or 25

Thunder gym: 27 or 28

Grass gym: 35 or 36

Poison gym 45 or 46

6 gym: 48 or. 50

Fire gym: 55

Ground gym: 60

Brock 14
Misty 20
Surge 24
Erika 30
Koga 38(at least)
Sabrina 43
Blaine 45
Giovanni 50 or 47(It depends if you have a water/grass or not if you do,do 47 so it's not too easy.

Elite 4 53(it's easy enough as long as you have a balanced team of at least 3 or 4 Pokemon. I used Charizard, Jolteon, Vileplume and Dugtrio.

For Brock if you choose charmander as your starter about level 12 or 13 but should probably catch a nidoran or mankey to get a fighting type move (Both nidoran and mankey learn fighting type moves early) If you chose squirtle or bulbasaur only level 10 or 11 (the only time it matters what starter you picked is the first gym since there are not many Pokemon that are good against rock early on)
For misty 20 through 22 (hint:catch an oddish on the route behind nugget bridge)
For Lt. Surge 23 through 25
For Erika about 28 through 31
For Koga at least 39 through 42 if not higher (hint: catch a kadabra or evolve an abra)
For sabrina 40 through 44 (you actually probably don't have to level up anymore from the last gym)
For Blaine 45 through 49
For giovani 46 through 50 (barely any harder than Blaine)

I beat brock with a level 6 mankey and went through other games with relative low levels relying on typing but that screwed me over at elite 4